MIAMI — In a bid to remake Florida’s judiciary, Republicans are asking voters to oust three state Supreme Court justices and give the Legislature greater power over Supreme Court appointments and judicial rules of procedure.

The campaign against the justices by Republican state party officials, a conservative group founded by the Koch brothers and a grass-roots group is similar to the successful push by conservative activists in Iowa during the 2010 election. Voters there defeated three Iowa Supreme Court justices over a ruling that allowed same-sex marriage in the state. A fourth Iowa justice who also ruled in the case is being targeted for ouster this year.

In Florida, the issue is not same-sex marriage but another politically divisive matter: President Obama’s health care law. In a 2010 ruling, the Florida Supreme Court removed from the ballot a nonbinding amendment allowing Floridians to refuse to buy mandatory health insurance. The justices ruled that the required ballot summary contained “misleading and ambiguous language” and asked the Legislature to fix it. Lawmakers did, and it is back on the ballot this year.

The initial ruling was one of several, including decisions on redistricting and property taxes and, going back to 2000, the ballot recount in Bush v. Gore, that have displeased conservatives in the state and in the Republican-dominated Legislature, which has tried since then to exert greater control over the court.

“I am very, very stressed at the entire circumstance,” said Justice R. Fred Lewis, one of the three judges targeted in the campaign. “What is going on now is much larger than any one individual. This is a full-frontal attack — that had been in the weeds before — on a fair and impartial judicial system, which is the cornerstone and bedrock of our democracy.”

The other two justices being targeted are Peggy A. Quince and Barbara J. Pariente. Justice Lewis and Justice Pariente were named by Gov. Lawton Chiles, a Democrat. Justice Quince was chosen by both Mr. Chiles and Jeb Bush during the 1998 transition. No justice has ever lost a retention battle. All three of these justices were returned to the bench in 2000 and again in 2006.

Florida Supreme Court justices appear on the ballot every six years as part of a system of merit retention. Floridians are asked to vote yes or no on whether the justices should remain on the bench. The system of selecting and retaining justices and appellate judges based on competence, and not politics, was put into place in the 1970s after a series of scandals involving popularly elected partisan judges. Until recently, the process was widely praised and largely free of politicking. But in 2010 that began to change.

This year, the campaign in Florida is considerably more intense and organized. For the first time, the Florida Republican Party’s executive board announced last week it would oppose the retention of the three justices because of their extensive “judicial activism.”

It singled out a 2003 case in which the court reversed the murder conviction of a man who tied a woman to a tree and set her on fire, and ordered a retrial on technical grounds. The United States Supreme Court reversed the decision, saying the justices had applied the wrong standard, and remanded the case to the Florida court. Ultimately, the conviction was affirmed, and the man remains on death row. By announcing its opposition to the three justices, the Republican Party avoids clashing with a law that prevents political parties from endorsing judicial candidates. In its statement, the party said the justices were “too extreme not just for Florida, but for America, too.”

Typically, decisions to remove a justice are based on misconduct or incompetence, not disagreements over particular decisions. The party’s decision to take sides surprised even some Republicans, who said it set a bad precedent.

“I think it’s a mistake for a party, as a party, to state a position that a certain judge should be thrown out, because then you are introducing partisanship into a system that is supposed to be nonpartisan,” said Bob Martinez, a prominent Republican lawyer who was once the United States attorney for the Southern District of Florida. “And when you have elected officials, on the right or left, criticizing judges publicly it can become very dangerous and it can undermine the public’s faith in the judiciary.”

Democrats say the campaign is really about giving Gov. Rick Scott, a Republican, the chance to appoint three new justices. The Florida Legislature also wants greater control of the judiciary — an effort that began last year with House Speaker Dean Cannon and is continuing with a proposed amendment on the ballot this year.

“All of this is an attempt to hijack the court,” said Dick Batchelor, a Democrat and former State House member who is working with Defend Justice From Politics, one of several counteroffensives. “This is all about raw politics. It has nothing to do with jurisprudence.”

Americans for Prosperity, an organization founded by the Koch brothers, recently joined in the battle and began broadcasting television advertisements in several cities highlighting the health care amendment ruling. The group also plans to highlight other cases.

“The Florida Supreme Court removed the amendment from the ballot, denying us a voice and a vote on a historically important issue,” the ad states. “Shouldn’t our courts be above politics and protect our rights to choose? You be the judge.”

Slade O’Brien, the Florida director of Americans for Prosperity, said the television spots, which do not explicitly take sides in the retention battle, focus attention on cases in which the court has acted as “judicial activists.”

Spearheading the battle over the justices is Restore Justice 2012, a grass-roots campaign that began its initial shoestring effort in 2010 and is taking its message to Tea Party activists around the state. The group released a video on the murder ruling this week. (Click on the top one.)

The three justices said in interviews that the decisions in question, including the nine-year-old murder conviction reversal, have been misconstrued to score political points. Critics disagree.

But the justices, while novices on the stump and restricted by judicial rules on campaigning, are amassing their own supporters. Sandra Day O’Connor, the retired United States Supreme Court justice, made a video for the Florida Bar Association’s Web site about the retention battle’s significance in Florida. (Under “Know the Facts,” click on the video.)

“Judicial independence is very hard to create and establish, and easier than most people imagine to damage and destroy,” she said.

Other supporters include the fire and police unions, which spoke out this week; the 23 past presidents of the Florida Bar Association; and a number of prominent Democrats in the state.

To counter the campaign, judges are being forced to raise money, which could lead to the perception they are beholden to donors. The justices’ three separate political committees have raised a total of about $1 million so far. They also could be accused of ruling on politically sensitive cases for the wrong reasons. Judicial rules also restrict what they can say in a campaign.

“It’s like getting into a fight with two hands behind your back tied and one leg,” Justice Pariente said. “We are trying to keep the high road.”

The Legislature is also involved in efforts to influence the judiciary. A ballot initiative, Amendment 5, would give the Senate, not the governor, final approval over the choice of State Supreme Court justices — similar to the federal system. It also would allow the Legislature to repeal court rules with a majority vote, not the two-thirds now required. And it would grant the House speaker access to confidential judicial misconduct investigation files before charges actually being filed.

A version of this article appears in print on October 3, 2012, on page A20 of the New York edition with the headline: G.O.P. Aims to Remake Florida Supreme Court. Order Reprints|Today's Paper|Subscribe